Learning is not Linear
Learning takes place OVER time while teaching takes place IN time
Research has shown that often when learners are working on one topic, some other topic, technique or concept may become clearer, even when it is not obviously connected to the current topic! (Brown et al)
Main Section
If you want learners to automate a procedure or technique, then give them a task in which, in order to find out what is going on (see Specialising & Generalising) they find themselves constructing particular examples for themselves on which they need to use the procedure or technique.
If you want learners to become familiar with the use of some technical language associated with a topic, give them tasks which are efficiently done when they use that language to talk to themselves and to compare notes with colleagues.
The metaphor of phase transition from physics is often appropriate in learning mathematics: sometimes energy put in is not manifested in observable change for a time (in physics the energy is achieving a change of state from solid to liquid or liquid to gas). In education, teacher attention and learner tasks may not result in improved performance for a time, and then suddenly there can be a major change in performance.
In adult education, we are always seeking to enable learners to generalise their learning and apply it in the real world. We call this transferability of skills. Hence real life examples, project work and discussion of wider issues is a genuine form of assessment of progress made in understanding and skills.
Often we only know there has been a real break through when we listen in to adult learners conversations about what they have learned and how they have applied it.
Probes & Prompts
When does learning take place? Can you catch moment when you actually learn something? What does it mean to learn something?
What is the burden of proof that an adult has learned something? The official line may be, when they have taken an adult numeracy test or passed from one curriculum level to the next. However, the real test is asking how they apply the new skill in practice.
Taking Action
With colleagues, work out what you would consider to be evidence that someone has learned a particular topic or technique. Then try to catch moments when you think someone actually learns it.
Set up conversation time in an adult numeracy session, when learners talk about how they have used what they have learnerd in real life.
Case Studies
Research Sources
Smith, Anderson et al 2004
Simon et al
Trimming: simplify presentation of ideas to make sense to learners, yet mathematically sound (Ferrini-Mundi in prep; Bruner Theory of Instruction S))
Categories
Curriculum, FAQs, Pedagogy